f(x) = (5x^3 + 1)^8 (4x^5 + 3)^7
How do I apply the chain rule to a problem like this?
Assuming you want to differentiate it, read it as a two-part product, apply the product rule, and each time you do a differentiation for the sake of the product rule you'll need to apply the chain rule - because each of the two parts of the product is a composite. Will put a pic, in a minute.
Just in case a picture helps...
... where (key in first spoiler)...
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Alternatively, take logs of both sides, then differentiate...
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Then solve the bottom row for f'(x).
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!